Home Page of Alberto Bressan

Position

Information:

• Office: room 201 McAllister Building
• Office phone: (814) 865 1667
• Fax: (814) 865 3735

Teaching and mentoring:

• Some research topics for graduate students' dissertations (pdf file)

Publications and CV:

• My CV (pdf-file) and list of publications (pdf-file).

Books:

• Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem (bookcover.html).
• Introduction to the Mathematical Theory of Control (bookcover.pdf), (Contents and Introduction.ps), (errata.pdf).

Most of my papers on hyperbolic conservation laws are available on the NTNU preprint server (Trondheim, Norway).

My recent papers on optimization and control theory are available on the IAC preprint server (Rome, Italy).

Areas of current research:

• Hyperbolic systems of conservation laws and nonlinear wave equations.
• Impulsive control of Lagrangian system. Stabilization and optimal control by moving constraints. Applications to swim-like motion in perfect fluids.
• Systems of Hamilton-Jacobi equations related to non-cooperative differential games. Nash equilibrium solutions in feedback form for infinite-horizon, discounted differential games. Applications to games of optimal inventory and pricing, in economics.
• Dynamic blocking problems (mathematical models of wild fire confinement). Existence of blocking strategies. Optimization problems.
• Optimization problems for elliptic equations, with measure-valued control strategies. Applications to optimal fishery management.

Some survey papers and tutorials:

• Lecture notes on hyperbolic systems of conservation laws,
  notes for a summer course, Cetraro 2009.
  (pdf-file, 84 pages)
• Viscosity solutions of nonlinear hyperbolic systems
  Proceedings HYP2002, Pasadena.
  (pdf-file, 21 pages)
• Hyperbolic systems of conservation laws in one space dimension
  Proceedings International Congress of Mathematicians, Beijing 2002.
  (pdf-file)
• Symmetries and blow up patterns
  A short tutorial, SISSA 1999.
  (ps-file, 17 pages) (pdf-file)
• Hamilton Jacobi Equations and Optimal Control
  An illustrated tutorial, Trondheim, NTNU 2001.
  (ps-file, 42 pages) (pdf-file)
• Lecture Notes on the Center Manifold Theorem
  S.I.S.S.A., 2003.
  (ps-file, 16 pages) (pdf-file)
• Notes on the Boltzmann equation
  lecture notes for a summer course, S.I.S.S.A., 2005.
  (ps-file, 28 pages) (pdf-file)
• BV solutions to hyperbolic system by vanishing viscosity
  Lecture notes for a C.I.M.E. course, 2003.
  (ps-file, 77 pages) (pdf-file)
• Impulsive control of Lagrangian systems and locomotion in fluids
  (pdf-file, 34 pages)

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Some other papers, preprints:

• On differential systems with vector-valued impulsive control
  (with F.Rampazzo) (pdf-file, 16 pages)
• Extremal selections of multifunctions generating a continuous flow
  (with G.Crasta) (pdf-file, 17 pages)
• Differential inclusions and the control of forest fires
  (pdf-file, 27 pages)
• Measure valued solutions for a differential game related to fish harvesting
  (with W.Shen) (pdf-file, 20 pages)
• Moving constraints as stabilizing controls in classical mechanics
  (with F.Rampazzo) (pdf-file, 44 pages)
• Classical solutions to differential inclusions with totally disconnected right hand side
  (with Z.Wang) (pdf-file, 11 pages)
• Existence of optimal strategies for a fire confinement problem
  (with C.De Lellis) (pdf-file, 40 pages)
• On the controllability of Lagrangian systems with active constraints
  (with Z.Wang) (pdf-file, 22 pages)
• Equivalent formulation and numerical analysis of a fire confinement problem
  (with T.Wang) (pdf-file, 32 pages)
• The minimum speed for a blocking problem on the half plane
  (with T.Wang) (pdf-file, 18 pages)
• From optimal control to non-cooperative differential games: a homotopy approach
  (pdf-file, 23 pages)
• Bifurcation analysis of a noncooperative differential game with one weak player
  (pdf-file, 19 pages)